nLab (infinity,n)-topos

Definition

For $\mathbf{H}$ an (∞,1)-topos and $n \in \mathbb{N}$, the collection $n Cat(\mathbf{H})$ of n-category object in $\mathbf{H}$, hence of (∞,n+1)-sheaves on $\mathbf{H}$ is an $(\infty,1)$-localic $(\infty,n+1)$-topos.

See at Internal category object in an (∞,1)-category – Iterated internalization.

Related concepts

• directed homotopy type theory

• locally presentable (∞,n)-category

flavors of higher toposes

• 1-topos

  • (0,1)-topos

  • (1,1)-topos = topos

  • (2,1)-topos

  • $(n,1)$-topos

  • (∞,1)-topos ($n$-localic)

    $\;\;\;\;$ model topos

• 2-topos

  • (2,2)-topos ($n$-localic)

  • (∞,2)-topos

• $n$-topos

  • $(\infty,n)$-topos